We shed new light on the negative relationship between real stock returns or real interest rates and (i) ex post inflation, (ii) expected inflation, (iii) unexpected inflation and (iv) changes in expected inflation. Using the structural vector autoregression methodology, we propose a decomposition of those series into economically interpretable components driven by aggregate supply, real demand and money market shocks. Our empirical results support Fama's 'proxy hypothesis' and the predictions of several general equilibrium models. Concerning the negative relation between the real rate of interest and inflation, we find that the Mundell-Tobin model and the explanation of Fama and Gibbons (1982) are not competitors: both add insight in their own way about the reasons for the negative correlation between those variables. However, the importance of the latter explanation has decreased since the 1980's.